The paper presents and discusses a method for rank-ordering alternatives on the basis of constraints induced by generic principles (expressing for instance the relative importance of criteria), or by examples of orderings between particular alternatives, without resorting to the use of an aggregation operation for evaluating the alternatives. The approach, which remains qualitative, is based on...

The paper presents the research results which can be applied in medicine: the fuzzy model of determination of severity of respiratory distress in a patient in an intensive care unit, based on the usage of a kind of fuzzy aggregation operator, the Choquet integral. The determination of the degree of respiratory distress is of extreme clinical relevance. The approach proposed in the paper is the ...

We propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also called Šipoš integral. Our framework is purely ordinal, since the Sugeno integral has its interest when the underlying structure is ordinal. We begin by defining negative numbers on a linearly ordered set, and we endow this new structure with a suitable algebra...

Every invariant biseparable preference relation can be represented by an integral on the set of continous a¢ ne mappings over a set of priors, where the integral is taken in the sense of Choquet. In looser terms: the representation takes the form of an integration over priors. As a by-product, we provide a novel interpretation of the (f)-MEU functional and of its relation with the Choquet integ...

In Song and Yan (2006), we introduced risk measures which are comonotonic subadditive or comonotonic convex, and gave their representations in terms of Choquet integrals. Independently, Heyde et al. (2006) proposed a data based risk measure in which the comonotonic subadditivity is taken as an axiom. The present paper proposes an axiomatic approach to some new risk measures and gives their repr...

We propose to extend the aggregation scheme of Saaty’s AHP, from the standard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the consistency case....

This paper establishes an evaluation system based on the low-carbon intensive land use in Jinan city from 2010 to 2017 and uses a multi-attribute approach named grey fuzzy integral build model. In this model, Mobius transformation coefficient of subjective objective weights index factors interaction degree between factors, 2-additive measures can be obtained; therefore, is processed by combinin...

We consider a collection F of subsets of a finite set N together with a capacity v : F → R+ and call a function f : N → R measurable if its level sets belong to F . Only in this case, the classical definition of the Choquet integral works in our wider context. In this article, we provide a general framework for a Choquet integral that works also for non-measurable functions f and includes the i...

In this paper we show how the distribution of the discrete Choquet integral can be analytically computed. The advantage of having an analytical expression is that the value of the cumulative distribution function (cdf) can be computed exactly for the Choquet. We also derive an expression for the density of the Ordered Weighted Average (OWA) operator, which is a special case of the Choquet.